若α∈(-π/2,0) sinα=-4/5 则tan(α+π/4)
问题描述：
若α∈(-π/2,0) sinα=-4/5 则tan(α+π/4)
答
解
a∈(-π/2,0)
∴cosa>0
∵sina=-4/5
∴cosa=√1-(-4/5)²=3/5
∴tana=sina/cosa=-4/3
∴tan(a+π/4)
=(tana+tanπ/4)/(1-tanatanπ/4)
=(-4/3+1)/(1+4/3)
=-1/3×3/7
=-1/7